Abstract
Oscillators under nonlocal couplings are systematically studied. We propose functions of inverse power as mathematical realization for nonlocal couplings among oscillators in a system. Power β in a function is taken as an important parameter in our study. Since its value determines a measure of "localization" while oscillators are nonlocally coupled it is then called the "nonlocal parameter". Together with the "phase lag parameter" α, which is vital for the existence of chimera states, we are able to demonstrate a valuable phase portrait in the β-α space. System dynamics is discussed in this phase diagram analogous to phase transitions in thermodynamics.
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